Two electrons in a quantum dot (QD) can form triplet states. We analyze the exchange coupling of the triplet states of the negatively charged exciton in a QD (${\mathrm{X}}^{-}$, two electrons and one hole) with the spin of a magnetic atom (Mn). Two techniques are used to access the spin structure of this magnetic complex: the resonant excitation of the excited states of ${\mathrm{X}}^{-}$-Mn and the analysis of the emission of a negatively charged biexciton in a magnetic dot (${\mathrm{XX}}^{-}$-Mn). The photoluminescence (PL) excitation of ${\mathrm{X}}^{-}$-Mn reveals excited states with a circularly polarized fine structure which strongly depends on the Mn spin state $S_z$ and gives rise to negative circular polarization emission. This fine structure arises from the coupling of the triplet states of an excited charged exciton with the Mn atom (${\mathrm{X}}^{-*}$-Mn), and its $S_z$ dependence can be described by a spin effective model. The recombination of ${\mathrm{XX}}^{-}$-Mn leaves in the dot a charged exciton in its excited state, and the PL structure is controlled by the coupling of triplet states of ${\mathrm{X}}^{-*}$ with the Mn spin. An analysis of the polarization and magneto-optic properties of this emission gives access to the electron-hole exchange interaction within the triplet states. Comparing the fine structures of the singlet ${\mathrm{X}}^{-}$-Mn and of the triplets of ${\mathrm{X}}^{-*}$-Mn, we can independently study the different sources of anisotropy in the QD: the valence band mixing and the exchange interaction in an anisotropic potential.

Quantum-mechanical calculations of electron magnetotransport in graphene Fabry-Pérot interferometers are presented with a focus on the role of spatial structure of edge channels. For an interferometer that is made by removing carbon atoms, which is typically realized in nanolithography experiments, the constrictions are shown to cause strong interchannel scattering that establishes local equilibrium and makes the electron transport nonadiabatic. Nevertheless, two-terminal conductance reveals a common Aharonov-Bohm oscillation pattern, independent of crystallographic orientation, which is accompanied by single-particle states that sweep through the Fermi energy for the edge channels circulating along the physical boundary of the device. The interferometer constrictions host the localized states that might shorten the device or disrupt the oscillation pattern. For an interferometer that is created by electrostatic confinement, which is typically done in the split-gate experiments, electron transport is shown to be adiabatic with Aharonov-Bohm interference observable only at some ranges of magnetic field, with interfering path going through depletion regions. Interference visibility decays exponentially with temperature with a weaker dependence at low temperature.

The wavefront dislocation is an important and ubiquitous phenomenon in wave fields. It is closely related to the phase singularity in a wave function. Some recent studies have verified that the wavefront dislocations in the local density of states map can well manifest the intrinsic topological characteristics in graphene and some topological systems. Different from these previous schemes, we raise a transport method to measure such wavefront dislocations in monolayer and Bernal-stacked bilayer graphene. Combining analytical analysis and numerical calculation, we find phase singularities naturally appear in the transmission coefficients between different sublattices, due to the intervalley interference on the electron propagating paths. These phase singularities could contribute wavefront dislocations in the conductance map. Additionally, in bilayer graphene, the wavefront dislocations are found to remain robust even though the tip is coupled to multiple sublattices. Biased bilayer graphene is also explored. Our scheme provides a transport routine to explore valley-related topological properties of materials.

The simulation of strongly correlated quantum impurity models is a significant challenge in modern condensed matter physics that has multiple important applications. Thus far, the most successful methods for approaching this challenge involve Monte Carlo techniques that accurately and reliably sample perturbative expansions to any order. However, the cost of obtaining high precision through these methods is high. Recently, tensor train decomposition techniques have been developed as an alternative to Monte Carlo integration. In this study, we apply these techniques to the single-impurity Anderson model at equilibrium by calculating the systematic expansion in power of the hybridization of the impurity with the bath. We demonstrate the performance of the method in a paradigmatic application, examining the first-order phase transition on the infinite-dimensional Bethe lattice, which can be mapped to an impurity model through dynamical mean field theory. Our results indicate that using tensor train decomposition schemes allows the calculation of finite-temperature Green's functions and thermodynamic observables with unprecedented accuracy. The methodology holds promise for future applications to frustrated multiorbital systems, using a combination of partially summed series with other techniques pioneered in diagrammatic and continuous time quantum Monte Carlo.

Consider a set of quantum states $\left|\psi \right(x)\rangle$ parameterized by $x$ taken from some parameter space $M$. We demonstrate how all geometric properties of this manifold of states are fully described by a scalar gauge-invariant Bargmann invariant $P^{\left(3\right)}(x_1,x_2,x_3)=tr\left[P\left(x_1\right)P\left(x_2\right)P\left(x_3\right)\right]$, where $P\left(x\right)=\left|\psi \right(x)\rangle \langle \psi (x\left)\right|$ are the projectors. Mathematically, $P\left(x\right)$ defines a map from $M$ to the complex projective space $\mathbb{C}{P}^n$ and this map is uniquely determined by $P^{\left(3\right)}(x_1,x_2,x_3)$ up to a symmetry transformation. The phase $arg{P}^{\left(3\right)}(x_1,x_2,x_3)$ can be used to compute the Berry phase for any closed loop in $M$, however, as we prove, it contains other information that cannot be extracted from any Berry phase. When the arguments $x_i$ of $P^{\left(3\right)}(x_1,x_2,x_3)$ are taken close to each other, to the leading order, it reduces to the familiar Berry curvature $\omega$ and quantum metric $g$. We show that higher orders in this expansion are functionally independent of $\omega$ and $g$ and are related to the extrinsic properties of the map of $M$ into $\mathbb{C}{P}^n$ giving rise to new local gauge-invariant objects, such as the fully symmetric 3-tensor $T$. Finally, we show how our results have immediate applications to the modern theory of polarization, calculation of the electric current response to a modulated field and physics of flat bands.

We investigate the effect of surface reconstruction and strain on diffusion of adsorbed Ge atoms on $\mathrm{Ge}\left(111\right)\text{−}5\times 5$ and $\mathrm{Ge}\left(111\right)\text{−}7\times 7$ surfaces by means of first-principles calculations. Stable adsorption sites and their energies, diffusion paths, and corresponding activation barriers are reported. We demonstrate that the decisive migration path is located near the corner holes of surface structures, and they are associated with formation of weak bonds between the adsorbed Ge atom and surface dimers (within the $5\times 5$ or $7\times 7$ structures). The results show that Ge diffusion rates on $5\times 5$ and $7\times 7$ reconstructed $\mathrm{Ge}\left(111\right)$ surfaces should be similar. Conversely, the diffusion barrier on a compressively strained $\mathrm{Ge}\left(111\right)$ surface is considerably higher than that on a strain-free surface, thus explaining previous experimental results. Comparable diffusion rates on $5\times 5$ and $7\times 7$ reconstructed surfaces are explained by the identical local atomic arrangements of these structures. The increase of the migration barrier on a strained surface is explained by dimer bond strengthening upon surface compression, along with a weakening of bonds between the adsorbed Ge and dimer atoms.

In this work we investigate the effect of a constant external, or artificial, magnetic field on the nonlinear response of two-dimensional (2D) Weyl materials. We calculate the Landau levels for tilted cones in 2D Weyl materials by treating the tilting in a perturbative manner and employ perturbation theory to calculate the tilting-induced correction to the magnetic field induced Landau spectrum. We then calculate the induced current as a function of the tilting coefficients and extract the corresponding nonlinear signal. Then, we analyze how changing the tilting parameter affects the nonlinear signal. Our findings show the possibility of achieving a significant tunability of the nonlinear response by suitably engineering the orientation and degree of tilt of Dirac cones in 2D Weyl materials.

Localization in one-dimensional interacting systems can be caused by disorder potentials or non-Hermiticity. The former phenomenon is the many-body localization (MBL), and the latter is the many-body non-Hermitian skin effect (NHSE). In this work, we numerically investigate the interplay between these two kinds of localization, where the energy-resolved MBL arises from a deterministic quasiperiodic potential in a fermionic chain. We propose a set of eigenstate properties and long-time dynamics that collectively distinguish the two localization mechanisms in the presence of non-Hermiticity. By computing the proposed diagnostics, we show that the thermal states are vulnerable to the many-body NHSE while the MBL states remain resilient up to a strong non-Hermiticity. Finally, we discuss experimental observables that probe the difference between the two localizations in a non-Hermitian quasiperiodic fermionic chain. Our results pave the way toward experimental observations on the interplay of interaction, quasiperiodic potential, and non-Hermiticity.

Zintl-phase ${\mathrm{EuCd}}_2{\mathrm{As}}_2$ attracts much research interest because it has a potential of manifesting various ideal topological states under external parameters. Here, measurements of resistance, magnetization, Hall, and synchrotron x-ray diffraction at high pressures up to 50.8 GPa in diamond anvil cells are performed on high-quality ${\mathrm{EuCd}}_2{\mathrm{As}}_2$ single crystals that display a long-sought intrinsically insulating antiferromagnetic (AFM) ground state. From ambient pressure to 21.0 GPa, the AFM state of ${\mathrm{EuCd}}_2{\mathrm{As}}_2$ is stable and the AFM transition temperature of $\sim 9.5$ K is raised linearly at a rate of $\sim 1.90$ K/GPa. Meanwhile, the insulating conduction behavior is maintained despite that the whole resistance decreases remarkably. Beyond $\sim 24.0$ GPa, a ferromagnetic-like metallic state shows up, due to a trigonal $P\overline{3}m1$ to monoclinic $C2/m$ structural transition, and its transition temperature of $\sim 150$ K increases linearly at a rate of $\sim 0.69$ K/GPa. This high-pressure magnetic metallic state dominates over the pristine AFM insulating one upon completion of the structural transition around 40 GPa. Based on the present data, we construct a temperature-pressure phase diagram for the intrinsically insulating antiferromagnet ${\mathrm{EuCd}}_2{\mathrm{As}}_2$, which offers essential insights into the pressure-dependent evolutions of magnetic and transport properties and will stimulate further exploration of the interplay among magnetism and transport, as well as nontrivial topology rooted in their interactions.

Nonlinear Hall effects have been previously investigated in noncentrosymmetric systems for electronic systems. However, they only exist in metallic systems and are not compatible with ferroelectrics since these latter are insulators, hence limiting their applications. On the other hand, ferroelectrics naturally break inversion symmetry and can induce a nonzero Berry curvature. Here, we show that a nonvolatile electric-field control of heat current can be realized in ferroelectrics through the nonlinear phonon Hall effects. More precisely, based on the Boltzmann equation under the relaxation-time approximation, we derive the equation for nonlinear phonon Hall effects, and further show that the behaviors of nonlinear Hall effects for phonons (that are bosons) are very different from nonlinear Hall effects for electrons (that are fermions). Our work therefore provides a route for electric-field control of thermal Hall current in ferroelectrics.

Rare-earth iron borates, $R{\mathrm{Fe}}_3{\left({\mathrm{BO}}_3\right)}_4$ ($R$ = rare earth), are of considerable interest because of their structural and magnetic complexities due to the involvement of both $3d$ and $4f$ magnetic interactions in a helical lattice. Among them ${\mathrm{Ho}}_{0.5}{\mathrm{Nd}}_{0.5}{\mathrm{Fe}}_3{\left({\mathrm{BO}}_3\right)}_4$ has attracted the most attention, as it exhibits a multiferroic property with a large, spontaneous, and magnetic-field-induced electric polarization ($P$) below the antiferromagnetic transition temperature (${\mathrm{T}}_N\sim 32$ K). This compound has been reported to be noncentrosymmetric (nonpolar) down to the lowest temperature, and the origin of spontaneous electric polarization below ${\mathrm{T}}_N$ is not known. By utilizing temperature-dependent synchrotron x-ray powder diffraction, we report here the observation of structural phase transition, i.e., the lowering of crystal symmetry from $R32$ to $P{3}_{1}21$ below ${\mathrm{T}}_N$ in ${\mathrm{Ho}}_{0.5}{\mathrm{Nd}}_{0.5}{\mathrm{Fe}}_3{\left({\mathrm{BO}}_3\right)}_4$, which is further confirmed by single-crystal x-ray diffraction measurements as well as substantiated by dielectric and Raman spectroscopic results. With the help of x-ray resonant magnetic scattering, we have studied the element-specific magnetic ordering behavior, and by combining all the results, we show that the spontaneous electric polarization below the antiferromagnetic ordering transition emerges through the p-d hybridization mechanism associated with the ${\mathrm{FeO}}_6$ octahedra. The observations of subtle structural changes at low temperature and element-specific magnetic ordering behavior provide a comprehensive understanding of the multiferroicity in this family of compounds.

Coding metasurfaces with efficient procedures and simple elements have enabled a large number of novel functions in a digital manner. Designs combining coding and functional integration will undoubtedly enhance the efficiency and space utilization of compact systems. Here, we theoretically propose and numerically and experimentally demonstrate an all-passive reflective Janus coding acoustic metasurface, allowing two-faced direction-dependent coding in a decoupled manner. Exquisitely designed double-layer variable-pitch helical structures with smoothly varying acoustic impedance are used to obtain bianisotropic reflection phase responses, which can also be switched to bi-isotropic responses by changing the boundary conditions. The switchable Janus coding metasurface based on the phase state transitions can be programed to achieve switchable functions on one side without affecting the other side. For instance, the asymmetric and symmetric two-faced focusing and unidirectional switching of functions with coding metasurfaces are numerically and experimentally illustrated. We reveal the inherent essence of the structure-caused asymmetric responses and further pave a flexible way to obtain two-faced, independent wavefront operations and functional switching, which exhibit excellent potential for acoustic applications.

The concept of crystalline disclinations in solid-state physics has gained attention in recent years, particularly with a focus on two-dimensional $C_n$-symmetric topological crystalline insulators. Research in this area has revealed novel topological phases different from the traditional bulk-boundary correspondence, expanding the topological material family. However, there remains a need to investigate the bulk-disclination correspondence in three-dimensional topological semimetals. We present an example of a higher-order Dirac semimetal in acoustic crystals with central disclinations. Our simple model not only exhibits hinge modes in the vertical direction but also supports a robust one-dimensional disclination hinge state along the central bulk-hollow path. Simulations demonstrate that our structure is capable of realizing backscatter-free disclination and higher-order hinge waves under the same architecture. Our findings offer insight for potential applications in acoustic devices for sound wave propagation and manipulation, as well as for exploring more exotic high-performance three-dimensional acoustic metamaterials.

We propose a fully quantum-mechanical formalism for the temperature-gradient-induced orbital magnetoelectric effect in systems without spatial inversion symmetry, $\mathcal{P}$, and time-reversal symmetry $\mathcal{T}$. The effect consists of two parts, i.e., an extrinsic part and an intrinsic part. We demonstrate that for the intrinsic part, a correction from the orbital magnetic quadrupole moment besides the usual Kubo formula, is necessary to avoid an unphysical divergence at zero temperature and to satisfy the Mott relation. Furthermore, we show the classification table with the magnetic point group for the intrinsic and extrinsic effects. Finally, we analyze the intrinsic part in a $\mathcal{PT}$-symmetric model exhibiting an orbital magnetization order, i.e., a loop-current order, and demonstrate the enhancement near Dirac points. We believe these results will contribute to the detection and application of orbital magnetic moments beyond spin moments.

Unlike the Berry phase, the orbital angular momentum (OAM) of magnons with two-dimensional wave vector $\mathbf{k}$ in band $n$ is not gauge invariant for arbitrary phase ${\lambda }_n\left(\mathbf{k}\right)$ and so is not physically observable. However, by integrating the OAM over the orientation $\varphi$ of wave vector $\mathbf{k}$, we construct a gauge-invariant function $F_n\left(k\right)$. Like $F_n\left(k\right)$, the average OAM for magnon band $n$ in a circle of radius $k$ is also gauge invariant and can be directly observed. We demonstrate these results for a ferromagnet on a honeycomb lattice with Dzyalloshinskii-Moriya interactions between next-nearest neighbor spins. With wave vectors $\mathbf{k}$ restricted to the first Brillouin zone, the angular averaged OAM $F_n\left(k\right)$ then has opposite signs for lower and upper bands $n=1$ and 2 for all $k$.

We report the crystal structure, magnetic structure, magnetic properties, electrical- and magnetotransport properties, and heat capacity of the rare-earth transition-metal compound ${\mathrm{Pr}}_2{\mathrm{PdAl}}_7{\mathrm{Ge}}_4$. ${\mathrm{Pr}}_2{\mathrm{PdAl}}_7{\mathrm{Ge}}_4$ crystallizes in the noncentrosymmetric tetragonal structure $P\overline{4}{2}_{1}m$ (No. 113) with unit cell parameters $a=6.0059\left(3\right)\AA$ and $c=15.2278\left(13\right)\AA$. The Néel temperature $T_{\mathit{N}}$ of ${\mathrm{Pr}}_2{\mathrm{PdAl}}_7{\mathrm{Ge}}_4$ was determined to be 6 K by the temperature dependences of magnetization, heat capacity, and electrical resistivity. The magnetic-field-induced antiferromagnetic to ferromagnetic transition occurs for magnetic fields $H$ along both the $ab$ plane and the $c$ axis. The electrical resistivity shows a metallic behavior with an upturn at the ordering temperature due to a superzone gap. Negative linear magnetoresistance is observed since the magnetic field increases the order degree of the antiferromagnetic state, reducing the magnetic correlation scattering. Neutron powder diffraction experiments reveal that metallic ${\mathrm{Pr}}_2{\mathrm{PdAl}}_7{\mathrm{Ge}}_4$ has an unusual noncollinear commensurate antiferromagnetic structure with the propagation vector $\mathit{k}=(0,0,0.5)$. Magnetic Pr atom layers stack with the ABBA sequence along the $c$ axis. Within the layers, the Pr moments lie in the $ab$ plane, and the angle between the nearest-neighbor spins is $67.1^{\circ }$. This magnetic structure can well explain the magnetic properties of ${\mathrm{Pr}}_2{\mathrm{PdAl}}_7{\mathrm{Ge}}_4$.

The extended principle of superposition has been a touchstone of spin-glass dynamics for almost 30 years. The Uppsala group has demonstrated its validity for the metallic spin glass, CuMn, for magnetic fields $H$ up to 10 Oe at the reduced temperature $T_{\mathrm{r}}=T/T_{\mathrm{g}}=0.95$, where $T_{\mathrm{g}}$ is the spin-glass condensation temperature. For $H>10$ Oe, they observe a departure from linear response which they ascribe to the development of nonlinear dynamics. The thrust of this paper is to develop a microscopic origin for this behavior by focusing on the time development of the spin-glass correlation length, $\xi (t,t_{\mathrm{w}};H)$. Here, $t$ is the time after $H$ changes, and $t_{\mathrm{w}}$ is the time from the quench for $T>T_{\mathrm{g}}$ to the working temperature $T$ until $H$ changes. We connect the growth of $\xi (t,t_{\mathrm{w}};H)$ to the barrier heights $\mathrm{\Delta }\left(t_{\mathrm{w}}\right)$ that set the dynamics. The effect of $H$ on the magnitude of $\mathrm{\Delta }\left(t_{\mathrm{w}}\right)$ is responsible for affecting differently the two dynamical protocols associated with turning $H$ off (TRM, or thermoremanent magnetization) or on (ZFC, or zero-field-cooled magnetization). This difference is a consequence of nonlinearity based on the effect of $H$ on $\mathrm{\Delta }\left(t_{\mathrm{w}}\right)$. Superposition is preserved if $\mathrm{\Delta }\left(t_{\mathrm{w}}\right)$ is linear in the Hamming distance $\mathrm{Hd}$ (proportional to the difference between the self-overlap $q_{\mathrm{EA}}$ and the overlap $q\left[\mathrm{\Delta }\left(t_{\mathrm{w}}\right)\right]$). However, superposition is violated if $\mathrm{\Delta }\left(t_{\mathrm{w}}\right)$ increases faster than linear in $\mathrm{Hd}$. We have previously shown, through experiment and simulation, that the barriers $\mathrm{\Delta }\left(t_{\mathrm{w}}\right)$ do increase more rapidly than linearly with $\mathrm{Hd}$ through the observation that the growth of $\xi (t,t_{\mathrm{w}};H)$ slows down as $\xi (t,t_{\mathrm{w}};H)$ increases. In this paper, we display the difference between the zero-field-cooled ${\xi }_{\text{ZFC}}(t,t_{\mathrm{w}};H)$ and the thermoremanent magnetization ${\xi }_{\text{TRM}}(t,t_{\mathrm{w}};H)$ correlation lengths as $H$ increases, both experimentally and through numerical simulations, corresponding to the violation of the extended principle of superposition in line with the finding of the Uppsala Group.

Understanding the high-pressure behavior of ammonia hydrates is relevant for modeling the interior of solar and extrasolar icy bodies. We present here the results of high-pressure x-ray diffraction studies on ammonia-dihydrate (ADH) at room temperature (298 K) up to 112 GPa, employing both static and dynamic compression experiments performed in diamond anvil cells. The derived pressure-volume (P-V) compression curves are in excellent agreement regardless of the compression technique. In contrast to early theoretical predictions, our results indicate the stability of the disordered molecular alloy (DMA) phase, a body centered cubic (bcc) structure, and the absence of self-ionization in the investigated pressure range. By combining the P-V data from seven different compression runs, we derive the first equation of state for ADH-DMA based on the third-order Birch-Murnaghan formalism with best-fit parameters: $V_0=23.96\pm 0.03$ (${\AA }^3$/molecule), $B_0=9.95\pm 0.14$ GPa, and $B_0^{\prime }=6.59\pm 0.03$. The instantaneous bulk modulus directly derived from the quasicontinuous compression curves displays a smooth increase upon compression that further supports the absence of structural transitions.

We present a theoretical study of how a spatially varying quasiparticle velocity in honeycomb lattices, achievable using strained graphene or in engineered cold-atom optical lattices that have a spatial dependence to the local tunneling amplitude, can yield the Rindler Hamiltonian embodying an observer accelerating in Minkowski space-time. Within this setup, a sudden switch on of the spatially varying tunneling (or strain) yields a spontaneous production of electron-hole pairs, an analog version of the Unruh effect characterized by the Unruh temperature. We discuss how this thermal behavior, along with Takagi's statistics inversion, can manifest themselves in photoemission and scanning tunneling microscopy experiments. We also calculate the average electronic conductivity and find that it grows linearly with frequency $\omega$. Finally, we find that the total system energy at zero environment temperature looks like Planck's blackbody result for photons due to the aforementioned statistics inversion, whereas for an initial thermally excited state of fermions, the total internal energy undergoes stimulated particle reduction.

The challenging task of scaling down the size of the power saving electronic devices can be accomplished by exploiting the spin degree of freedom of the conduction electrons in van der Waals (vdW) spintronic architectures built with 2D materials. One of the key components of such a device is a near-room temperature 2D ferromagnet with good metallicity that can generate a highly spin-polarized electronic transport current. However, most of the known 2D ferromagnets have either a very low-temperature ordering, poor conductivity, or low spin polarization. In this context, the ${\mathrm{Fe}}_n{\mathrm{GeTe}}_2$ (with $n\ge 3$) family of ferromagnets stand out due to their near-room temperature ferromagnetism and good metallicity. We have performed spin-resolved Andreev reflection spectroscopy on ${\mathrm{Fe}}_4{\mathrm{GeTe}}_2$ ($T_{\mathrm{Curie}}\sim 273\mathrm{K}$) and demonstrated that the ferromagnet is capable of generating a very high transport spin polarization, exceeding $50\%$. This makes ${\mathrm{Fe}}_4{\mathrm{GeTe}}_2$ a strong candidate for application in all-vdW power-saving spintronic devices.